In this paper, we propose a new fast search algorithm for block motion estimation (BME). This algorithm employs two techniques: the center-biased technique and the two-path technique. The former is applied to stop the search procedure if the block currently being processed is stationary. Otherwise, the proposed algorithm conducts the two-path search to perform BME. The search result of the traditional one-path search will probably not reach the global minimum. It is clear that two-path search can reduce this bias. The experimental results show that the computational complexity of the proposed algorithm is low and that its image quality is acceptable no matter whether the input video contains slow motion only or a large amount of activity.